Comment on Poirer: The Subjective Perspective of a "Spiritual Bayesian"

[This paper responds to "Frequentist and Subjectivist Perspectives on the Problems of Model Building in Economics," by Dale J. Poirier, in this same issue.] Professor Dale Poirier has preached a rousing sermon for the Bayesian cause and in doing so has concisely exposed some of the cracks in the foundations of statistics. One of these cracks is the very interpretation of the concept of probability, a philosophical question that has never been fully resolved and has led to the schism that currently exists in statistics between the Bayesian and classical schools. The paper is valuable for econometricians because it challenges them to think more deeply about the meaning of the statistical procedures they employ. However a basic question was not addressed; namely, what is the purpose of statistical inference? I think the answer to this question has at least as much bearing upon whether someone adopts Bayesian or classical methodology as whether one interprets the meaning of probability in subjectivist or frequentist terms. I think that the purpose of statistical inference is to "learn." This view treats statistical inference as a process of formulating a sequence of models that are abstract but in some sense increasingly accurate representations of certain aspects of reality that we seek to understand. In the rest of this piece, I will discuss the limitations of Bayesian estimation theory and the limitations of Classical Estimation theory.